An open box with a volume of 1428 cm3 is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Show that this can be done in two different ways, and find the exact dimensions of the box in each case.

Question

campbell_st · Answer

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the length of the box is 40 - 2x
       width of the box is 20 - 2x
       height of the box is x

$$V = x \times (20 -2x) \times (40 - 2x)$$

and this is all equal to 1428

$$V = 4x^3 - 120x^2 + 800x - 1428$$